K-解析函数的Riemann边值问题

张建元; 赵书芬; 韩艳

doi:10.3879/j.issn.1000-0887.2014.07.010

K-解析函数的Riemann边值问题

doi: 10.3879/j.issn.1000-0887.2014.07.010

¹昭通学院数学与统计学院, 云南昭通 657000;²哈尔滨工业大学数学系,哈尔滨 150001

基金项目: 国家自然科学基金(11061028);云南省教育厅科学研究基金(2012Y435；2013Y578)

详细信息

作者简介:
张建元(1956—), 男, 云南昭通人, 教授（通讯作者. E-mail: zhangjianyuan07@163.com）

中图分类号: O174.55;O175.5
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- 被引次数: 0
出版历程
- 收稿日期: 2013-11-28
- 修回日期: 2014-05-27
- 刊出日期: 2014-07-15

Riemann’s Boundary Value Problem of K-Analytic Functions

¹School of Mathematics and Statistics, Zhaotong University, Zhaotong, Yunnan 657000, P.R.China;²Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China(11061028)

摘要

摘要: 引入了（分片）K-解析函数和Cauchy型K-积分的概念.利用K-对称变换的方法研究了Cauchy型K-积分的某些性质，然后借助函数在曲线上的指标与这些Cauchy型K-积分的性质，得到了K-解析函数类中的Riemann边值问题的可解条件和解的表达式以及它们与指标之间的关系.而解析函数和共轭解析函数都是K-解析函数的特例，文中所得结果，推广了解析函数和共轭解析函数中的相应结论.
- Cauchy型K-积分 /
- （分片）K-解析函数 /
- K-对称变换 /
- 边界值公式 /
- Riemann边值问题 /
- 指标
Abstract: First, the concepts of the (piecewise) K-analytic function and the Cauchy type K-integral were introduced, and some properties of the Cauchy type K-integral were studied through K-symmetry transformation. Then, with the function index of the curve and the properties of the Cauchy type K-integral, the solvable conditions and the solution expressions for the Riemann’s boundary value problem of the K-analytic function as well as the relationship between the solutions and the index were obtained. Since both the analytic functions and the conjugate analytic functions are special cases of the K-analytic functions, the present conclusions generalize many known related results of them.
- Cauchy type K-integral /
- (piecewise) K-analytic function /
- K-symmetry transformation /
- boundary value formula /
- Riemann’s boundary value problem /
- index

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参考文献(16)

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